Evolution of eigenvalue of the Wentzell–Laplace operator along the conformal mean curvature flow

Abstract

In this paper, we investigate continuity, differentiability and monotonicity for the first nonzero eigenvalue of the Wentzell–Laplace operator along the conformal mean curvature flow on $n$-dimensional compact manifolds with boundary for $n \geq 3$ under a boundary condition. In especial, we show that the first nonzero eigenvalue of the Wentzell–Laplace operator is monotonic under the conformal mean curvature flow and we find some monotonic quantities dependent to the first nonzero eigenvalue along the conformal mean curvature flow.